The 22nd International Conference on Machine Learning, August 2005 (talk)

Abstract

We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.

We discuss reproducing kernel Hilbert space (RKHS)-based measures of statistical dependence,
with emphasis on constrained covariance (COCO), a novel criterion to
test dependence of random variables. We show that COCO is a test for independence if and only if the associated RKHSs
are universal.
That said, no independence
test exists that can distinguish dependent and independent random variables in all circumstances. Dependent random variables can result in a COCO which is arbitrarily close to zero when the source densities are highly non-smooth. All current kernel-based independence tests share this behaviour. We demonstrate exponential convergence between the population and empirical COCO. Finally, we use COCO as a measure of joint neural activity between voxels in MRI recordings of the macaque monkey, and compare the results to the mutual information and the correlation. We also show the effect of removing breathing artefacts from the MRI recording.

2002

2002

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems